Muriel Humphrey yesterday accepted an offer to fill the Senate seat of her late husband, Hubert H. Humphrey, who died of cancer Jan. 13.

At the same time, she pointedly said she does not regard the post as "a caretaker job." She left open the door to a possible candidacy in November, when Minnesotans will vote in a special election to fill the remaining four years of Humphrey's six-year term.

"That's too far ahead for anybody to be thinking about right now," she said. "If I do a good job - that's my goal."

Humphrey, 65, appeared with Minnesota Gov. Rudy Perpich at a news conference in the lobby of an ocean-front apartment here, about 40 miles north of Maimi, where she has been vacationing since Saturday.

Perpich offered her the position during a morning meeting that lasted 1 1/2 hours.

"Muriel Humphrey should be appointed to the United States Senate because she, more than anyone else, could continue the programs and philosophy of Hubert Humphrey, the greatest public servant that Minnesota has ever produced," Perpich said in a statement.

The offer had been anticipated since last week. But it was widely thought that Humphrey would be asked to hold the job temporarily, with the Democratic-Farmer-Labor Party choosing another candidate for the November election.

Perpich, asked whether he and Humphrey discussed the coming election, replied, "No, we did not." And Humphrey seemed to keep her options open.

"I feel it was a very, very difficult decision to make, and a very responsible one to make," she said, "and I do not take it lightly - not as a caretaker job.

Fred Gates, who headed the late senator's Minneapolis office and who attended the private meeting this morning, said he would "presume that Humphrey was keeping her options open for November. Asked whether she had asked her husband's staff to stay on and work for her, Gates replied, "Pretty much so."

Humphrey would not be pinned down about what she might do in November. "That's a long time away," she said. "I have no idea."

She and her husband never discussed the possibility of her succeeding him, she said. "I think Hubertert never once said he was going to do anything but go back to the Senate. . . I had no guidance at all from him on the decision."

She added that "I am [WORD ILLEGIBLE] by my doctor that my health is [WORD ILLEGIBLE] and that there is every reason [WORD ILLEGIBLE] I can undertake these duties and discharge them in a vigorous manner."

Humphrey, who will be the only woman senator, plans to return to Washington after a "brief rest," including a few days in the Virgin Islands.

In Minnesota, her refusal to confine her Senate role to that of an interim caretaker threw the Democratic Farmer Labor Party into a turmoil.

Most immediately affected was Democratic Rep. Donald M. Fraser, who announced on Monday that he would be a candidate for the Humphrey seat. In a telephone interview yesterday, he said "I'm running all the way."

Perpich earlier left the impression that he was leaning strongly toward a caretaker senator. Earlier in the week he indicated he feared it would be a blunder to appoint a likely candidate in the November election. "Appointing that person might be like a kiss of death," he said alluding to criticism he suffered after Gov. Wendell R. Anderson resigned in December 1976 to have Perpich his successor, appoint him to the Senate seat being vacated by Walter F. Mondale, then the vice president-elect.

On the Republican side, state chairman Vern Neppl said the Democratic Farmer Labor Party was "arrogant and insensitive," adding "Perpich is responsible for the death of respresentative government in Minnesota. He holds the smoking gun."

Rep. Thomas M. Hagedorn (R-Minn.) said he admired Muriel Humphrey but said it looked aa though "we have moved into a state of monarchy."